Comment by Kim_Bruning

That's a very good US-side steelman!

The counter-argument, of course, is that a country is allowed to adjudicate crimes that happen inside their own borders, else what's even the point of being a country.

The ICC has been granted jurisdiction by it's 124 signatories, so if crimes against humanity occur within their borders, then -for those countries- the ICC acts as part of their court system. Uncomfortably, this includes Afghanistan and the Palestinian state, so you can see why respectively the USA and Israel might have some issues.

Of course it kind of helps if people are arrested on the ground in the country where they committed the crimes they are accused of. The ICC does not necessarily have the ability to reach into non-member states to arrest people who have left the scene of the crime. They can only issue a warrant on the off chance that one day those people step back into their jurisdiction.